Patients are randomized to 1 of 3 treatment groups and, within each group, are stratified by baseline FEV1 cohort. Patients receive either dose level 1 of IL-4R, dose level 2 of IL-4R, or placebo, by aerosol drug delivery device, once a week for 12 weeks. There are frequent clinic visits and several follow-up visits. Physical exams and spirometry are done regularly; immunizations are administered on Day 28; and a skin tests panel is given on Day 84. Blood samples are collected at study visits during treatment and follow-up to test for immunology/serology parameters, chemistry profiles, and asthma-related DNA polymorphisms. Patients are provided with peak flow meters and must demonstrate their proper use so that a peak expiratory flow (PEF) diary and a symptoms diary can be maintained. Selected sites measure exhaled nitric oxide and collect induced sputum samples. Assessments for adverse events are conducted at 16 and 40 weeks following the first study drug treatment.